Thanks for showing at least some work. But you have made a huge step going from your original circuit to you second circuit. What you ask someone to review your work (especially strangers who you aren't paying) you want to make it so that they can follow your work from step to step and verify that what you have done is valid without having to pull out a scratch pad and work the problem for themselves from scracth. BTW, if you take this approach with what you turn in, you will almost certainly see a significant improvement in the grades you get back -- it's part of the proper care and feeding of homework graders.

Now, consider your simplified circuit. You have a dependent source that is controlled by the current ix, but you don't give any indication of which current is ix. That should set off warning flags right there.

What efforts have you made to check your answer? One of the nice things about most engineering disciplines is that you can verify the validity of an answer by taking the answer as a given and showing that it is consistent with the original problem.

Neither answer is correct, but the other answer is (in some regards) very close.

Thanks for showing at least some work. But you have made a huge step going from your original circuit to you second circuit. What you ask someone to review your work (especially strangers who you aren't paying) you want to make it so that they can follow your work from step to step and verify that what you have done is valid without having to pull out a scratch pad and work the problem for themselves from scracth. BTW, if you take this approach with what you turn in, you will almost certainly see a significant improvement in the grades you get back -- it's part of the proper care and feeding of homework graders.

Now, consider your simplified circuit. You have a dependent source that is controlled by the current ix, but you don't give any indication of which current is ix. That should set off warning flags right there.

What efforts have you made to check your answer? One of the nice things about most engineering disciplines is that you can verify the validity of an answer by taking the answer as a given and showing that it is consistent with the original problem.

Neither answer is correct, but the other answer is (in some regards) very close.

Yes, that is correct. When I said that both answers were incorrect, I didn't see the negative sign on the -96V and so thought it said 96V. The price of going blind. Hope that didn't lead you too far astray.

The steps you showed were pretty reasonable, too.

The one thing that would have made it quicker to follow would have been to just note that you were doing a source transformation on the voltage source, because the way you showed it makes it easy for someone looking at it to be drawn into a conclusion that you were saying that the current in the 24Ω resistor is 4A (which is a common mistake because people see a voltage source next to a resistor and many will just through Ohm's law at it). It took seeing about three different peices, each of which individually would be a fairly common error, and realizing that they were all elements of one transformation. A simple note such as "Thev->Nort" would have made it obvious how to interpret what you were showing.

Now, having said that, you should take a step back and see that you could have written KVL for that node by inspection of the original circuit. Going from right to left.

8A + (Vab/16Ω) - 2(Vab/16Ω) - [(96V-Vab)/24Ω] + (Vab/16Ω) = 0

8A + (1-2+1)(Vab/16Ω) - (96V/24Ω) + (Vab/24Ω) = 0

(Vab/24Ω) = -8A + (96V/24Ω) = -8A + 4A = -4A

Vab = (-4A)(24Ω) = -96V

By drawing an arrow through the (96V/24Ω) and in the second line and indicating that it is 4A, you could safely eliminate the third line, or at least only have the far left side and the far right side.

Finally, I strongly, strongly, strongly urge you to get in the habit of always, always, ALWAYS, tracking your units through out your work and not just tacking what you believe are the correct units on at the end. Most mistakes you will make will screw up the units and let you catch the mistake immediately. At ANY point, if the units don't work out, you KNOW the answer is wrong.